# What is the coefficient of x^8y^5 in the expansion of (x+y)^{13}?

## Question:

What is the coefficient of {eq}x^8y^5 {/eq} in the expansion of {eq}(x+y)^{13} {/eq}?

## Binomial Theorem:

Any binomial expression can be simplified as per the following expression:

{eq}\large (x+y)^{n} = x^{n} + nx^{n-1}y + \frac{n(n-1)}{2!} x^{n-2} y^{2} + ..... + y^{n} {/eq}

The binomial coefficient is in the form of {eq}^nC_k {/eq} for any term {eq}x^k.y^{(n-k)} {/eq}

## Answer and Explanation:

In the expansion of {eq}(x+y)^{13} {/eq} we have the coefficient of {eq}x^8y^5 {/eq} as {eq}^{(8+5)}C_8 = ^{13} C_8=1287 \Rightarrow(Answer) {/eq}

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